An investigation of new associated curves of a Frenet curve in Euclidean n-space

ÖZÇETİN VATANSEVER B. M.

Turkish Journal of Mathematics, cilt.49, sa.6, ss.822-837, 2025 (SCI-Expanded, Scopus, TRDizin) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 49 Sayı: 6
  • Basım Tarihi: 2025
  • Doi Numarası: 10.55730/1300-0098.3627
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.822-837
  • Anahtar Kelimeler: 53A04, associated curve, Frenet curve, general helix, integral curve, slant helix
  • İstanbul Gelişim Üniversitesi Adresli: Evet

Özet

In this study, we introduce the V2-direction curve, Vn−1-direction curve and Vn-direction curve of a Frenet curve in n-dimensional Euclidean space. We provide characterizations and investigate the relationships between the Frenet apparatus of the principal curve and the corresponding apparatus of the direction curves. We also present an application for all direction curves with the results shown using computer code implemented in MATLAB.